Anomalous relaxation in quantum systems and the non-Markovian stochastic Liouville equation

TL;DR

This paper investigates anomalous relaxation in quantum systems caused by non-Markovian noise, deriving a stochastic Liouville equation that captures unique relaxation behaviors under subdiffusive and slowly decaying noise conditions.

Contribution

It introduces a non-Markovian stochastic Liouville equation derived from continuous time random walk approach for quantum relaxation under anomalous noise.

Findings

Reveals specific features of quantum relaxation with anomalous noise

Derives a non-Markovian stochastic Liouville equation for density matrices

Analyzes two models: two-level system and radical pair recombination

Abstract

The kinetics of relaxation in quantum systems induced by anomalous fluctuating noise is studied in detail. In this study two processes are considered, as examples: (1) relaxation in two-level system caused by external noise with slowly decaying correlation function P (t) ~ (wt)^{-alpha}, where 0 < alpha < 1, and (2) anomalous-diffusion controlled radical pair recombination in which relaxation results from the reaction with slowly fluctuating reaction rate whose fluctuations are governed by subdiffusive relative motion of radicals in a potential well. Analysis of these two processes is made within continuous time random walk approach (CTRWA). Rigorous CTRWA-treatment of the processes under study results in the non-Markovian stochastic Liouville equation (SLE) for the density matrix of the systems. This SLE predicts important specific features of relaxation kinetics of quantum systems in the presence of the above mentioned anomalous noise.